Electro-optic modulators are well known and one of the well-known deficiencies of electro-optic modulators is the inefficient transduction from the electrical signal to the modulated optical signal. This weakness arises because the needed modulation-control voltage of prior art modulators is so high; generally at least several volts is needed to achieve full on-off modulation. Optical ring resonators and optical disk resonators based on whispering-gallery modes propagating near the perimeter of the disks have been used in prior electro-optic modulators as a means to reduce the needed modulation-control voltage.
A prior concept for a modulator based on an input/output waveguide that is coupled to an optical-waveguide ring resonator (see FIG. 1a) is described by A. Yariv in a paper and a patent application (A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photonics Technology Letters, vol. 14, 2002, p. 483; and A. Yariv, “Optical routing/switching based on control of waveguide-ring resonator coupling,” US2001/0004411). Most examples of fabricated modulators of this type are based on control of the resonator resonance frequency or loss.
An example of a prior art modulator having an input/output waveguide coupled to a microdisk resonator is illustrated in FIG. 1b. This modulator is described in a paper by L. Zhou and A. W. Poon (“Silicon electro-optic modulators using p-i-n diodes embedded 10-micron-diameter microdisk resonators,” Optics Express, vol. 14, no. 15 (2006), p. 6851). The refractive index of the microdisk material is modulated by an applied voltage and thus the resonance wavelength of the resonator is modulated. Although this modulator has a bandwidth of 510 MHz, its full-scale modulation-control voltage exceeds 7 volts.
Another example of a prior modulator has a traveling-wave electrode connected to the ring resonator itself to modulate the resonance wavelength of that resonator, as shown in FIGS. 2a, 2b1 and 2b1. This prior modulator is described in papers by H. Tazawa, et al. (“Ring resonator-based electrooptic polymer traveling-wave modulator,” J. Lightwave Technology, vol. 24, 2006, p. 3514) and by B. Bortnik, et al. (“Electrooptic polymer ring resonator modulation up to 165 GHz,” IEEE J. Selected Topics in Quantum Electronics, vol. 13, no. 1 (2007), p. 104). Although this modulator can have modulation response at certain very high frequencies (e.g., 28 or 165 GHz), the modulation bandwidth is limited to at most several GHz and the full-scale modulation-control voltage is greater than 7 volts.
A modulator based on control of coupling between an input/output waveguide and a ring resonator also is described in the aforementioned publications by Yariv. A prior modulator based on this concept of waveguide-resonator coupling was constructed and is described in a paper by W. M. J. Green et al. (“Hybrid InGaAsP—InP Mach-Zehnder racetrack resonator for thermooptic switching and coupling control,” Optics Express, vol. 13, 2005, p. 1651). This prior art modulator contains a 2×2 Mach-Zehnder Interferometer (MZI) as the coupler and an input segment plus an output segment of that MZI are connected together by a feedback loop to form the ring resonator (see FIG. 3). However, the modulation bandwidth measured was only 400 kHz. The two electrodes modulate the two arms of the MZI to control the coupling to/from the feedback loop. These bulk electrodes use the thermo-optic effect to modulate the refractive index of the two MZI arms by changing their temperature.
Yet another prior art modulator has part of its MZI in a circular ring resonator, as illustrated in FIG. 4. This modulator is described in a patent issued to W. K. Burns, et al. (“High gain resonant modulator system and method,” U.S. Pat. No. 7,262,902 B2, issued 28 Aug. 2007). One arm of the MZI, two fixed-ratio couplers of the MZI and the feedback path are part of the ring resonator. A second arm of the MZI, with that second arm being much longer than the first arm, is part of a separate loop. In order to achieve push-pull modulation of the two arms of its MZI, this modulator must be used together with an electronic inverter that causes the phases of the voltage waveforms applied to the two electrodes coupled to those two arms to be opposite. The two electrodes, used for electro-optic modulation, are bulk electrodes (in contrast to traveling-wave electrodes such as those of Tazawa et al. or Bortnik et al.) and their large capacitance could limit the modulation bandwidth.
In papers by Sacher and Poon (“Dynamics of microring resonator modulators,” Optics Express, vol. 16, 2008, p. 15741; and “Characteristics of microring resonators with waveguide-resonator coupling modulation,” J. Lightwave Technology, vol. 27, 2009, p. 3800), those authors point out that the limited modulation bandwidth of an electro-optic modulator with an optical resonator occurs because the resonance wavelength of the resonator itself is modulated. Sacher and Poon also explained that high modulation efficiency (i.e., having strong modulation of the output light produced by a low RF-modulation-control voltage or RF power) can be obtained when the resonator has low loss or high Q, a condition which was not achieved in the device reported by Green, et al. Also, the authors point out that large modulation bandwidth can be achieved if the free spectral range (FSR) of the resonator is large. Modulation with relatively wide bandwidth and with low distortion is achievable for a modulator having a high-Q resonator when the laser wavelength corresponds to a resonance wavelength of the resonator and when the modulation frequency components are not close to an integer multiple of the FSR, unlike the modulators of Tazawa and Bortnik. One kind of distortion is a memory effect that arises from modulation of the intensity of the light recirculating in the resonator loop. For a 2×2 MZI coupled resonator, the 2×2 MZI could be modulated in push-pull manner so that the modulator output is not chirped and so that the linearity of the modulation response is improved.
However, for the prior art 2×2 MZI coupled microring resonator of Green, et al. (see FIG. 3), the FSR of that resonator is very small because the 2×2 MZI itself is long and the loop resonator involves a combination of straight optical waveguide segments and curved optical waveguide segments whose loss would be very high if their radius of curvature is too small. The prior modulator of Burns, et al. (see FIG. 4) can have a short resonator loop that has low loss. Although the modulator of Burns, et al. can provide push-pull modulation, that push-pull modulation is achieved by applying separate voltages of opposite polarity to the two bulk electrodes controlling the phase modulation of the two interferometer arms, which have very unequal path length. There could easily be a net modulation of the phase of the light coupled from that asymmetric MZI into the recirculation path (labeled as 117 of FIG. 4) in the ring resonator. Any net phase modulation could greatly limit the modulation bandwidth of this modulator. The patent of Burns, et al. does not contain any mention of avoiding modulation of the resonance frequencies or resonance wavelengths of its ring resonator.
Thus, the need remains for a modulator that is compact, has low full-scale modulation voltage (preferably less than 2 volts) and large modulation bandwidth (preferably greater than 1 GHz), and that also can be modulated with high-frequency signals of 10 GHz and higher.